{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "\n",
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "</p>\n",
    "\n",
    "## Linear Regression in Python for Engineers, Data Scientists and Geoscientists \n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "#### Contacts: [Twitter/@GeostatsGuy](https://twitter.com/geostatsguy) | [GitHub/GeostatsGuy](https://github.com/GeostatsGuy) | [www.michaelpyrcz.com](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446)\n",
    "\n",
    "This is a well-documented demonstration of **Linear Regression** in Python with the SciPy package, [Stats](https://docs.scipy.org/doc/scipy/reference/stats.html) module.    \n",
    "\n",
    "This demonstration includes basic, calculation of a linear regression model (only 1 predictor and 1 response), model visualization and checking, hypothesis testing the significance of the parameters, calculation the parameter confidence intervals and the prediction intervals.\n",
    "\n",
    "##### My Other Resources\n",
    "\n",
    "I have not included all the details, e.g., for the test assumptions in this document. These are the related lectures with linked Python interactive dashboards and well-documented demonstrations (like this one):\n",
    "\n",
    "* [Bivariate Statistics](https://youtu.be/wZwYEDqB4A4)\n",
    "* [Q-Q plots](https://youtu.be/RETZus4XBNM) \n",
    "* [Linear Regression](https://youtu.be/HzWq7pj2F_w) \n",
    "* [Norms](https://youtu.be/JmxGlrurQp0)\n",
    "\n",
    "#### Load the required libraries\n",
    "\n",
    "The following code loads the required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os                                                   # to set current working directory \n",
    "import numpy as np                                          # arrays and matrix math\n",
    "import scipy.stats as st                                    # statistical methods\n",
    "from sklearn.linear_model import LinearRegression           # scikit-learning multilinear regression\n",
    "import pandas as pd                                         # DataFrames\n",
    "import matplotlib.pyplot as plt                             # for plotting\n",
    "plt.rc('axes', axisbelow=True)                              # set axes and grids in the background for all plots\n",
    "import math                                                 # for square root"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you get a package import error, you may have to first install some of these packages. This can usually be accomplished by opening up a command window on Windows and then typing 'python -m pip install [package-name]'. More assistance is available with the respective package docs.  \n",
    "\n",
    "#### Declare Functions\n",
    "\n",
    "For the more complicated operations (e.g., prediction intervals), I made functions for readable code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the working directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time).  Also, in this case make sure to place the required (see below) data file in this working directory.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#os.chdir(\"C:\\PGE337\")                                      # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Using You Own Data\n",
    "\n",
    "I have set up this workflow so you can easily replace my provided demonstration dataset with your own data.\n",
    "\n",
    "1. Replace the file to load below with your own file. You could load from the cloud or a local file, I have provided examples for both.\n",
    "\n",
    "2. Below, specify the column from your DataFrame below for the predictor feature, X, and the response feature, y.\n",
    "\n",
    "3. Also, set the range of the predictor and response features for plotting,and the features' name and features' units.\n",
    "\n",
    "#### Loading Data\n",
    "\n",
    "Let's load the provided dataset. 'Density_Por_data.csv' is available at https://github.com/GeostatsGuy/GeoDataSets. It is a comma delimited file with 105 porosity and density measures from a rock unit.\n",
    "\n",
    "* density ($g/cm^3$)\n",
    "* porosity ($\\%$). \n",
    "\n",
    "We load it with the pandas 'read_csv' function into a data frame we called 'df' and then preview it by printing a slice and by utilizing the 'head' DataFrame member function (with a nice and clean format, see below)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Density</th>\n",
       "      <th>Porosity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.281391</td>\n",
       "      <td>16.610982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.404932</td>\n",
       "      <td>13.668073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.346926</td>\n",
       "      <td>9.590092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.348847</td>\n",
       "      <td>15.877907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.331653</td>\n",
       "      <td>4.968240</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Density   Porosity\n",
       "0  1.281391  16.610982\n",
       "1  1.404932  13.668073\n",
       "2  2.346926   9.590092\n",
       "3  1.348847  15.877907\n",
       "4  2.331653   4.968240"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#df = pd.read_csv(\"Density_Por_data.csv\")                    # read a .csv file in as a DataFrame\n",
    "df = pd.read_csv(r\"https://raw.githubusercontent.com/GeostatsGuy/GeoDataSets/master/Density_Por_data.csv\") # load data from Dr. Pyrcz's GitHub repository\n",
    "df.head()                                                    # we could also use this command for a table preview "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is useful to review the summary statistics of our loaded DataFrame.  That can be accomplished with the 'describe' DataFrame member function.  We transpose to switch the axes for ease of visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Density</th>\n",
       "      <td>105.0</td>\n",
       "      <td>1.737917</td>\n",
       "      <td>0.288278</td>\n",
       "      <td>0.996736</td>\n",
       "      <td>1.552713</td>\n",
       "      <td>1.748788</td>\n",
       "      <td>1.906634</td>\n",
       "      <td>2.410560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Porosity</th>\n",
       "      <td>105.0</td>\n",
       "      <td>12.531279</td>\n",
       "      <td>3.132269</td>\n",
       "      <td>4.966421</td>\n",
       "      <td>10.546483</td>\n",
       "      <td>12.411608</td>\n",
       "      <td>14.230930</td>\n",
       "      <td>20.964941</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          count       mean       std       min        25%        50%  \\\n",
       "Density   105.0   1.737917  0.288278  0.996736   1.552713   1.748788   \n",
       "Porosity  105.0  12.531279  3.132269  4.966421  10.546483  12.411608   \n",
       "\n",
       "                75%        max  \n",
       "Density    1.906634   2.410560  \n",
       "Porosity  14.230930  20.964941  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe().transpose()                                    # calculate summary statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we extract the samples from the DataFrame into separate 1d ndarrays called 'por' and 'den' for convenience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predictor feature: Density, label: Density ($g/cm^3$)\n",
      "Response feature: Porosity, label: Porosity (%)\n"
     ]
    }
   ],
   "source": [
    "y = df['Porosity'].values                                  # shallow copy features to 1D ndarrays for convenience \n",
    "yname = 'Porosity'; yunits = '%'\n",
    "ylabel = 'Porosity ('+ yunits +')'\n",
    "ymin = 0.0; ymax = 25.0\n",
    "X = df['Density'].values; xunits = '$g/cm^3$'\n",
    "xname = 'Density'; \n",
    "xlabel = 'Density (' + xunits + ')'\n",
    "xmin = 1.0; xmax = 2.4\n",
    "dX = np.linspace(xmin,xmax,100)                              # a 1D array of 100 density values for calculation and plotting\n",
    "\n",
    "print('Predictor feature: ' + xname + ', label: ' + (xlabel))\n",
    "print('Response feature: ' + yname + ', label: ' + ylabel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear Regression Model\n",
    "\n",
    "Let's first calculate the linear regression model, a model object from SciPy package, stats module.\n",
    "\n",
    "This is our model:\n",
    "\n",
    "\\begin{equation}\n",
    "por = b_1 \\times den + b_0\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Output from linregress function is <class 'scipy.stats._stats_mstats_common.LinregressResult'>:\n",
      "LinregressResult(slope=-9.103894698738019, intercept=28.353094840583744, rvalue=-0.8378757673511419, pvalue=7.744611355360021e-29, stderr=0.5844011014765733, intercept_stderr=1.02938720863459)\n",
      "\n",
      "Linear Regression Model:\n",
      "  Slope: -9.1\n",
      "  Intercept: 28.35\n",
      "  Square Root of R-squared: -0.84\n",
      "  Slope p-value: 0.0\n",
      "  Slope standard error: 0.58\n"
     ]
    }
   ],
   "source": [
    "linear = st.linregress(X,y)                              # output is the linear regression model\n",
    "print('\\nOutput from linregress function is ' + str(type(linear)) + ':')\n",
    "print(linear)\n",
    "print('\\nLinear Regression Model:')\n",
    "print('  Slope: ' + str(round(linear.slope,2)))\n",
    "print('  Intercept: ' + str(round(linear.intercept,2)))\n",
    "print('  Square Root of R-squared: ' + str(round(linear.rvalue,2)))\n",
    "print('  Slope p-value: ' + str(round(linear.pvalue,2)))\n",
    "print('  Slope standard error: ' + str(round(linear.stderr,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualize the Linear Regression Model\n",
    "\n",
    "Now let's visualize the linear regression model with the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The model parameters are, slope (b1) = -9.1, and the intercept (b0) = 28.35\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('The model parameters are, slope (b1) = ' + str(round(linear.slope,2)) + ', and the intercept (b0) = ' + str(round(linear.intercept,2)))\n",
    "plt.scatter(X, y, color = 'darkorange',edgecolor='black',alpha=0.8,label='sample data',zorder=10)\n",
    "plt.plot(dX, linear.intercept + linear.slope*dX, 'black', label='linear regression model',zorder=1)\n",
    "plt.title('Sample Data and Linear Regression Model'); plt.xlabel(xlabel); plt.ylabel(ylabel)\n",
    "plt.legend(); plt.grid(); plt.ylim([ymin,ymax]); plt.xlim([xmin,xmax])\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.4, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Confidence Intervals\n",
    "\n",
    "Let's calculate the 95% confidence interval for the linear regression model slope parameter, $b_1$, of our model.\n",
    "\n",
    "\\begin{equation}\n",
    "CI_{\\hat{b_1}}: \\hat{b}_1 ± t_{(\\frac{\\alpha}{2},n-2)} \\times SE_{b_1} \n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "CI_{\\hat{b_0}}: \\hat{b}_0 ± t_{(\\frac{\\alpha}{2},n-2)} \\times SE_{b_0} \n",
    "\\end{equation}\n",
    "\n",
    "where standard errors are calculated as:\n",
    "\n",
    "\\begin{equation}\n",
    "SE_{b_1} = \\frac{\\sqrt{n}\\hat{\\sigma}}{\\sqrt{n-1} \\sqrt{\\sum(x_i - \\overline{x})^2  } }\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "SE_{b_0} = \\sqrt{ \\frac{\\hat{\\sigma}^2}{n-2} }\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The model parameters confidence intervals at a 0.95 significance level are:\n",
      "Slope: P2.5 = -10.26 , P97.5 = -7.94\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "tstat = st.t.ppf([alpha/2,1-alpha/2], len(X)-2)            # calculate t-stat for confidence interval\n",
    "slope_lower,slope_upper = linear.slope + tstat*linear.stderr # calculate the lower and upper confidence interval for b1\n",
    "#intercept_lower,intercept_upper = linear.intercept + tstat*linear.intercept_stderr # \"\" for b0\n",
    "\n",
    "print('The model parameters confidence intervals at a ' + str(1-alpha) + ' significance level are:')\n",
    "print('Slope: P' + str(alpha/2*100) + ' = '+ str(round(slope_lower,2)) + ' , P' + str((1-alpha/2)*100) + ' = ' + str(round(slope_upper,2)))\n",
    "#print('Intercept: ' + str(round(intercept_lower,2)) + ' , ' + str(round(intercept_upper,2)))\n",
    "\n",
    "plt.scatter(X, y, color = 'darkorange',edgecolor='black',alpha=0.8,label='sample data',zorder=10)\n",
    "plt.plot(dX, linear.intercept + linear.slope*dX, 'black', label='linear regression model')\n",
    "plt.plot(dX, linear.intercept + slope_upper*dX, 'black',ls='--',lw=1,label=r'alpha = ' + str(alpha) + ' confidence interval')\n",
    "plt.plot(dX, linear.intercept + slope_lower*dX, 'black',ls='--',lw=1)\n",
    "plt.fill_between(dX,linear.intercept + slope_upper*dX,linear.intercept + slope_lower*dX,color='red',alpha=0.3,zorder=1)\n",
    "plt.title('Sample Data, Linear Regression Model and Slope Confidence Intervals'); plt.xlabel(r'Density ($g/cm^3$)'); plt.ylabel('Porosity (%)')\n",
    "plt.legend(loc='lower left'); plt.grid(); plt.ylim([ymin,ymax]); plt.xlim([xmin,xmax])\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.4, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Prediction Intervals\n",
    "\n",
    "Let's calculate the prediction intervals.\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{y}_{n+1} ± t_{(\\frac{\\alpha}{2},n-2)} \\sqrt{MSE}\\ \\times \\sqrt{1+\\frac{1}{n}+\\frac{(x_{n+1}-\\overline{x})^2}{\\sum_{i=1}^{n}(x_{i}-\\overline{x})^2}  }\n",
    "\\end{equation}\n",
    "\n",
    "Note, this is the standard error of the prediction:\n",
    "\n",
    "\\begin{equation}\n",
    "SE_{\\hat{y}_{n+1}} = \\sqrt{MSE}\\ \\times \\sqrt{1+\\frac{1}{n}+\\frac{(x_{n+1}-\\overline{x})^2}{\\sum_{i=1}^{n}(x_{i}-\\overline{x})^2}  }\n",
    "\\end{equation}\n",
    "\n",
    "where MSE, model mean square error calculated as:\n",
    "\n",
    "\\begin{equation}\n",
    "MSE = \\sum_{i=1}^n\\frac{(y_i - \\hat{y}_i)^2}{n-2} = \\sum_{i=1}^n \\frac{\\left(y_i - (b_1 x - b_0) \\right)^2}{n-2}\n",
    "\\end{equation}\n",
    "\n",
    "Note, that this indicates that prediction intervals are wider the further we estimate from the mean of the predictor feature values. We can substitute model MSE, MSE, and standard error of the estimate, $SE_{\\hat{y}_{n+1}}$ for the final form is:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{y}_{n+1} ± t_{(\\frac{\\alpha}{2},n-2)} \\sqrt{\\sum_{i=1}^n \\frac{\\left(y_i - (b_1 x - b_0) \\right)^2}{n-2}}\\sqrt{1+\\frac{1}{n}+\\frac{(x_{n+1}-\\overline{x})^2}{\\sum_{i=1}^{n}(x_{i}-\\overline{x})^2}  }\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For the alpha level of: alpha = 0.05, \n",
      "the t-statistic is: -1.98\n",
      "\n",
      "For the prediction at: X = 1.5, \n",
      "the standard error of the prediction is: 1.73\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_X = 1.5\n",
    "alpha = 0.05\n",
    "\n",
    "tstat = st.t.ppf([alpha/2,1-alpha/2], len(X)-2)\n",
    "\n",
    "print('For the alpha level of: alpha = ' + str(alpha) + \\\n",
    "      ', \\nthe t-statistic is: ' + str(round(tstat[0],2)))\n",
    "\n",
    "yhat = linear.intercept + linear.slope*X\n",
    "MSE = np.sum(np.power(y-yhat,2))/(len(y)-2) # mean square error\n",
    "est_stderr = math.sqrt(MSE) \\\n",
    "      *math.sqrt(1 + 1/len(y) + np.power(new_X - np.average(X),2)/ \\\n",
    "      np.sum(np.power(X-np.average(X),2)))\n",
    "\n",
    "print('\\nFor the prediction at: X = ' + str(new_X) + \\\n",
    "      ', \\nthe standard error of the prediction is: ' + str(round(est_stderr,2)))\n",
    "\n",
    "y_pred_lower, y_pred_upper = linear.intercept + linear.slope*new_X + tstat*est_stderr\n",
    "\n",
    "plt.scatter(X, y, color = 'darkorange',edgecolor='black',alpha=0.8,label='sample data',zorder=1)\n",
    "plt.plot(dX, linear.intercept + linear.slope*dX, 'black', label='linear regression model',zorder=1)\n",
    "plt.scatter(new_X, linear.intercept + linear.slope*new_X,s=80,color='yellow',edgecolor='black',label='prediction, $\\hat{y}$',zorder=2)\n",
    "plt.plot([new_X,new_X],[y_pred_lower,y_pred_upper],color='black',linestyle='dashed',zorder=1,label='prediction interval')\n",
    "plt.title('Sample Data, Linear Regression Model and Prediction Interval'); plt.xlabel(r'Density ($g/cm^3$)'); plt.ylabel('Porosity (%)')\n",
    "plt.legend(); plt.grid(); plt.ylim([4,22]); plt.xlim([1.0,2.4])\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.4, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the prediction interval over the entire range of possible predictions and compare with the confidence interval.\n",
    "\n",
    "* we will also plot the standard error of the estimate to show the subtle heteroscedasticity of the prediction interval, the prediction error increases away from the mean of predictor feature values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.05\n",
    "\n",
    "tstat = st.t.ppf([alpha/2,1-alpha/2], len(X)-2)   \n",
    "slope_lower,slope_upper = linear.slope + tstat*linear.stderr  # confidence interval\n",
    "\n",
    "yhat = linear.intercept + linear.slope*X                 \n",
    "MSE = np.sum(np.power(y-yhat,2))/(len(X)-2)            # prediction interval: model MSE\n",
    "    \n",
    "y_pred_lower_mat = np.zeros(len(dX)); y_pred_upper_mat = np.zeros(len(dX))\n",
    "est_stderr_mat = np.zeros(len(dX))\n",
    "\n",
    "for inew_X, new_X in enumerate(dX):\n",
    "    est_stderr_mat[inew_X] = math.sqrt(MSE) * math.sqrt(1 + 1/len(X) + np.power(new_X - np.average(X),2)/np.sum(np.power(X-np.average(X),2)))\n",
    "    y_pred_lower_mat[inew_X], y_pred_upper_mat[inew_X] = linear.intercept + linear.slope*new_X + tstat*est_stderr_mat[inew_X]\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(dX,est_stderr_mat,c='r',ls='--',lw=1,label='standard error of the prediction')\n",
    "plt.plot([np.average(X),np.average(X)],[1.7,1.8],c='black',lw=1)\n",
    "plt.annotate('Prediction Feature Mean',[np.average(dX)*0.98,1.767],rotation=90)\n",
    "plt.title('Standard Error of the Estimate vs. Predictor Value'); plt.xlabel(r'Density ($g/cm^3$)'); plt.ylabel('Standard Error of the Prediction, Porosity (%)')\n",
    "plt.legend(loc='lower left'); plt.grid(); plt.xlim([xmin,xmax]); plt.ylim([1.7,1.8])\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(dX, linear.intercept + linear.slope*dX, 'black', label='linear regression model')\n",
    "plt.plot([np.average(X),np.average(X)],[ymin,ymax],c='black',lw=1)\n",
    "plt.annotate('Prediction Feature Mean',[np.average(X)*0.98,16],rotation=90)\n",
    "plt.plot(dX,y_pred_lower_mat,c='black',lw=1,zorder=1)\n",
    "plt.plot(dX,y_pred_upper_mat,c='black',lw=1)\n",
    "plt.fill_between(dX,y_pred_upper_mat,y_pred_lower_mat,color='red',alpha=0.3,zorder=1,label=r'alpha = ' + str(alpha) + ' prediction interval')\n",
    "\n",
    "plt.plot(dX, linear.intercept + slope_upper*dX, 'black',lw=1,ls='-.')\n",
    "plt.plot(dX, linear.intercept + slope_lower*dX, 'black',lw=1,ls='-.')\n",
    "plt.fill_between(dX,linear.intercept + slope_upper*dX,linear.intercept + slope_lower*dX,color='black',alpha=0.3,zorder=1,label=r'alpha = ' + str(alpha) + ' confidence interval')\n",
    "plt.title('Linear Regression Model, Confidence Interval and Prediction Interval'); plt.xlabel(r'Density ($g/cm^3$)'); plt.ylabel('Porosity (%)')\n",
    "plt.legend(); plt.grid(); plt.ylim([ymin,ymax]); plt.xlim([xmin,xmax])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.4, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Checking\n",
    "\n",
    "Let's test the slope with the following hypothesis test:\n",
    "\n",
    "\\begin{equation}\n",
    "H_0: b_{1} = 0.0\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "H_1: b_{1} \\ne 0.0\n",
    "\\end{equation}\n",
    "\n",
    "and see if we can reject this hypothesis, $H_{0}$ , that the slope parameter is equal to 0.0.  If we reject this null hypothesis, we show that the slope is meaning full and there is a linear relationship between density and porosity that we can use.\n",
    "\n",
    "Fortunately, the linregress function from the stats module of SciPy package provides us with the two sided p-value for this test.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The linear regression model slope parameter p-value is 0.0.\n"
     ]
    }
   ],
   "source": [
    "print('The linear regression model slope parameter p-value is ' + str(round(linear.pvalue,20)) + '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's calculate the $r^2$, proportion of variance explained. Here's the variance explained by the model:\n",
    "\n",
    "\\begin{equation}\n",
    "𝑠𝑠𝑟𝑒𝑔 = \\sum_{𝑖=1}^{𝑛}\\left(\\hat{y}_i - \\overline{y}\\right)^2 \n",
    "\\end{equation}\n",
    "\n",
    "and the variance not explained by the model:\n",
    "\n",
    "\\begin{equation}\n",
    "𝑠𝑠𝑟𝑒sid = \\sum_{𝑖=1}^{𝑛}\\left(y_i - \\hat{y}\\right)^2 \n",
    "\\end{equation}\n",
    "\n",
    "Now we can calculate the variance explained as:\n",
    "\n",
    "\\begin{equation}\n",
    "𝑟^2 = \\frac{𝑠𝑠𝑟𝑒𝑔}{𝑠𝑠𝑟𝑒𝑔+𝑠𝑠𝑟𝑒𝑠𝑖𝑑} = \\frac{\\text{variance explained}}{\\text{total variance}}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The r-squared value of the linear regression model is 0.702\n"
     ]
    }
   ],
   "source": [
    "r2 = linear.rvalue**2\n",
    "print('The r-squared value of the linear regression model is ' + str(round(r2,3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's perform a f-test for the significance of all model parameters at once.\n",
    "\n",
    "\\begin{equation}\n",
    "H_0: b_i = 0, \\forall i\n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "H_1: otherwise\n",
    "\\end{equation}\n",
    "\n",
    "To test this hypothesis we calculate the $f_{statistic}$ and $f_{critical}$ as:\n",
    "\n",
    "\\begin{equation}\n",
    "f_{statistic} = \\frac{\\text{Mean Squares of Model}}{\\text{Mean Squares of Error}}   \n",
    "\\end{equation}\n",
    "\n",
    "\\begin{equation}\n",
    "f_{statistic} = \\frac{ \\frac{\\sum_{𝑖=1}^{𝑛}(\\hat{y}_i - \\overline{y})^2}{k-1} } { \\frac{\\sum_{𝑖=1}^{𝑛}\\left(y_i - \\hat{y}\\right)^2}{n-k} }\n",
    "\\end{equation}\n",
    "\n",
    "and now we can calculate the $f_{critical}$ value as:\n",
    "\n",
    "\\begin{equation}\n",
    "𝑓_{𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙}  = f_{k-1,n-k}(1-𝛼)\n",
    "\\end{equation}\n",
    "\n",
    "Since this is a one-tail test, if $f_{statistic} > f_{critical}$, then we reject the null hypothesis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The f-stat is : 345.68 and the f-critical is : 3.933\n",
      "Therefore we reject the null hypothesis, \n",
      "our model parameters are significant\n"
     ]
    }
   ],
   "source": [
    "alpha = 0.05                                                 # alpha level, 1 - confidence level\n",
    "k = 2                                                        # number of model parameters\n",
    "ms_model = np.sum(np.power(y-np.average(y),2))/(k-1)     # f-test, calculate f-stat and f-critical\n",
    "ms_error = np.sum(np.power(y-yhat,2))/(len(y)-k)\n",
    "f_stat = ms_model/ms_error                                   \n",
    "f_crit = st.f.ppf(1-alpha, k-1, len(y)-k)\n",
    "\n",
    "print('The f-stat is : ' + str(round(f_stat,2)) + ' and the f-critical is : ' + str(round(f_crit,3)))\n",
    "\n",
    "if f_stat > f_crit:\n",
    "    print('Therefore we reject the null hypothesis, \\nour model parameters are significant')\n",
    "if f_stat <= f_crit:\n",
    "    print('Therefore we fail to reject the null hypothesis, \\nour model parameters are NOT significant')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Correlation Coefficient\n",
    "\n",
    "We can also observe correlation coefficient.\n",
    "\n",
    "* valid and useful for our linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The correlation coefficient is = -0.84\n"
     ]
    }
   ],
   "source": [
    "print('The correlation coefficient is = ' + str(round(linear.rvalue,2))) # correlation coefficient"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Cross Validation\n",
    "\n",
    "Let's use this model to make a prediction at all the data locations.  \n",
    "\n",
    "* now plot a standard model cross validation plot, actual vs. predicted values for the response feature\n",
    "* note, we are only looking at data used to build the model, known as training data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.05                                                 # alpha level, 1 - confidence level\n",
    "yhat = linear.slope * X + linear.intercept              # estimate at the training data location\n",
    "plt.scatter(yhat,y,color='darkorange',alpha=0.8,edgecolor='black')\n",
    "plt.plot([ymin,ymax],[ymin,ymax],color='black',linewidth=1)\n",
    "plt.ylabel('Actual ' + ylabel ); plt.xlabel('Estimated ' + ylabel ); \n",
    "plt.title('Training Data Cross Validation Plot')\n",
    "plt.xlim(ymin,ymax); plt.ylim(ymin,ymax)\n",
    "plt.grid(); plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.4, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's look at the distribution of estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(yhat,color='darkorange',alpha=0.4,edgecolor='black',bins=np.linspace(ymin,ymax,30),label='Predictions')\n",
    "plt.hist(y,color='grey',alpha=0.4,edgecolor='black',bins=np.linspace(ymin,ymax,30),label='Data')\n",
    "plt.title(yname + \" Predictions with Linear Model\")\n",
    "plt.xlabel(ylabel); plt.ylabel('Frequency'); plt.legend(loc='upper right')\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is useful to plot the predictions of porosity and porosity data vs. the density data. From this plot we can observe the linear limitation of our model and get a sense of the unexplained variance $\\frac{\\sum_{i=1}^{n}(y_i - \\hat{y}_i)^2} {n-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, y,color='black',alpha=0.8,facecolor='grey',label='sample data',zorder=10)\n",
    "plt.scatter(X, yhat,color='black',s=40,facecolor='darkorange',alpha=0.8,label='model',zorder=10)\n",
    "plt.plot(dX, linear.intercept + linear.slope*dX, 'black', label='linear regression model',zorder=1)\n",
    "\n",
    "for i in range(0,len(X)):\n",
    "    plt.plot([X[i],X[i]],[y[i],yhat[i]],c='grey',alpha=0.8,ls='--',zorder=1)\n",
    "plt.title('Sample Data and Model'); plt.xlabel(xlabel); plt.ylabel(ylabel)\n",
    "plt.legend()\n",
    "plt.grid(True); plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next let's calculate the residual and check their distribution. \n",
    "\n",
    "* residuals are the true values at the data locations minus the estimates at the data locations, $y_i - \\hat{y}_i$.  \n",
    "\n",
    "We want to make sure the average is close to 0.0 (unbiased estimates) and to observe the shape and spread of the residual distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The average of the residuals is 0.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "residual = y - yhat\n",
    "plt.hist(residual,color='darkorange',alpha=0.8,edgecolor='black',bins=np.linspace(-5,5,30))\n",
    "plt.title(\"Residual\")\n",
    "plt.xlabel(yname + ' True - Estimate ' + yunits)\n",
    "plt.grid(True)\n",
    "print('The average of the residuals is ' + str(round(np.mean(residual),2)))\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we will check the residual vs. the fitted value.  \n",
    "\n",
    "* we want to see if the errors are consistent over the range of fitted values.  \n",
    "\n",
    "* for example, we could use this plot to identify higher error or systematic under- or overestimation over a specific range of fitted values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(yhat,residual,facecolor='darkorange',alpha=0.8,color='black')\n",
    "plt.title('Residual vs. Fitted Value')\n",
    "plt.xlabel(yname + ' Estimate (%)')\n",
    "plt.ylabel(yname + ' Residual (%)')\n",
    "plt.plot([5,20], [0,0],'black')\n",
    "plt.grid(True); plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let's Rebuild the Model with scikit-learn\n",
    "\n",
    "* scikit-learn is one of the most popular Python machine learning packages\n",
    "\n",
    "* demonstrates the standard scikit-learn approach\n",
    "\n",
    "1. **instantiate** - make the model object while setting the hyperparameters (none for linear regression)\n",
    "2. **fit** - train the model parameters with training data (we aren't doing train and test split yet) \n",
    "3. **predict** - use the trained model to make predictions (for demonstration we just predict at the training data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_model = LinearRegression()                           # instantiate the prediction model\n",
    "linear_model.fit(X.reshape(-1, 1),y)             # train the model with the training data\n",
    "yhat_scikit = linear_model.predict(X.reshape(-1, 1)) #$ predict with the trained model\n",
    "\n",
    "plt.scatter(X, y,color='black',alpha=0.8,facecolor='grey',label='sample data',zorder=10)\n",
    "plt.scatter(X, yhat_scikit,color='black',s=40,facecolor='darkorange',alpha=0.8,label='model',zorder=10)\n",
    "plt.plot(dX, linear.intercept + linear.slope*dX, 'black', label='linear regression model',zorder=1)\n",
    "\n",
    "for i in range(0,len(X)):\n",
    "    plt.plot([X[i],X[i]],[y[i],yhat_scikit[i]],c='grey',alpha=0.8,ls='--',zorder=1)\n",
    "    \n",
    "plt.title('Sample Data and scikit-learn Model'); plt.xlabel(xlabel); plt.ylabel(ylabel)\n",
    "plt.legend()\n",
    "plt.grid(True); plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.1, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of linear regression in Python with the SciPy package.\n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  }
 ],
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